CUAE211_ELECTRICAL MACHINES

3.2.TRANSFORMERS

Level: 2.2 Date:

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 Presentation Layout
 Learning Outcomes
 Introduction
 Phasor diagram and equivalent circuit of transformer
 Referred values
 Voltage Regulation
 Open circuit test and short circuit test
 Transformer losses and Efficiency

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 Learning Objectives
1. Describe transformer equivalent circuit and phasor
diagram
2. Explain the open circuit and short circuit tests
3. Describe the losses which occur in transformer
4. Calculate transformer efficiency and regulation
5. Describe the construction of Autotransformer.

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 Practical Transformer
Certain assumptions made for an ideal
transformer are not valid in a practical
transformer.
In practical transformer :
(i) the windings have resistance
(ii) core has finite permeability
(iii) there is leakage flux
(iv) efficiency is not 100% due to losses
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Complete circuit model (equivalent circuit)
of a real transformer

Cooper losses are modeled by the resistors Rp and Rs.

The leakage flux can be modeled by primary and secondary
inductors, Xp and Xs .
The magnetization current can be modeled by a reactance XM
connected across the primary voltage source.
The core-loss current can be modeled by a resistance RC
connected across the primary voltage source.
Equivalent circuit of Real Transformer
 Referred values
 In order to simplify calculations, it is theoretically
possible to transfer voltage, current and impedance
of one winding to the other and combine them into
single value for each quantity.

 Let R2’ be the resistance of the secondary

resistance R2 referred to the primary winding.

 R2’ should produce the same effect in the primary

as R2 produces in the secondary.

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 Referred values
Power consumed by R2’ when carrying the primary
current should be equal to the power consumed by
R2 due to secondary current

I R  I R2
1
2 '
2
2
2
2
 I2 
R 
 I 
'
2  R2
 1
 R2 k 2 Since:

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 Referred values
Similarly , let X2’ the reactance of the secondary
winding referred to the primary side.
For X2’ to produce the same effect in the primary
side as X2 in the secondary side, each must
absorb the same reactive voltamperes (VAr)

I12 X 2'  I 22 X 2
2
 I2 
X 
 I 
'
2  X2 Since:
 1 
 X 2k 2
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 Equivalent values referred to primary
2
V 
Re1  R1  R2 '  R1  R2  1   R1  R2 k 2
 V2 
2
V 
X e1  X 1  X 2 '  X 1  X 2  1   X 1  X 2k 2
 V2 

2
V 
Z e1  Z1  Z 2'  Z1  Z 2  1   Z1  Z 2 k 2
 V2 
Where magnitude of Ze
In complex notation:
Ze = Re+ jXe Ze  Re2  X e2

Re  Ze cose X e  Z e sin e
Xe
tan e 
Re
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 Equivalent values referred to secondary
The equivalent values referred to the secondary
can also be found in the same manner.
If Re2 , Xe2 and Ze2 denote the equivalent
resistance, equivalent reactance and equivalent
impedance respectively referred to the
secondary, then: 2
 V2  R1
Re 2  R2  R1'  R2  R1 
V 
  R2  2
 1  k
2
 V2  Z1
Z e 2  Z 2  Z1'  Z 2  Z1 
V 
  Z 2  2
 1  k

2
 V2  X1
X e 2  X 2  X 1'  X 2  X 1 
V 
  X 2  2
 1  k
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 Equivalent circuit of transformer
 Approximate equivalent circuit referred to the primary can be
derived from complete equivalent circuit as follows:
(i) referred to primary as the square of the transformation ratio:
R2 k2 R2
X2 k2 X2
ZL k2 ZL

(ii) all voltages are referred directly as the product of the

transformation ratio:
V2 k V2
E2 k E2
(iii) All secondary currents are referred to the primary inversely
as the transformation ratio: I2
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 Equivalent circuit of transformer
 The approximate equivalent circuit of
the transformer referred to the
secondary can be determined in the
same manner:
(i) R1, X2 and ZL are multiplied by
(ii) V1 and E1 are multiplied by
(iii) I1 is multiplied by

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 The exact equivalent circuit of a real
transformer
The transformer’s equivalent
circuit (a)

However, the exact circuit is

not very practical.
Equivalent circuit of the transformer referred
Therefore, the equivalent circuitside.
to its primary is
usually referred to the primary side or
the secondary side of the transformer.
(b)

Equivalent circuit of the

transformer referred to its
primary side
Equivalent circuit of the transformer referred (c)
Equivalent
to circuit
its secondary side.of the
transformer referred to its
secondary side
 Approximate equivalent circuit of a
transformer
For many practical applications, approximate models of transformers are used.

(a) (b)
Referred to Referred to
the primary the
side. secondary
side.

(c) (d)

Without an excitation Without an excitation

branch referred to the branch referred to the
primary side. secondary side.
 Voltage regulation
 Voltage regulation (VR) is the ability of a system to provide
near constant voltage over a wide range of load conditions.
 Mathematically voltage regulation is defined as below:

Ideal transformer, VR = 0%.

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 Transformer Phasor Diagram
To determine the voltage regulation of a transformer, it
is necessary understand the voltage drops within it.

Based upon the equivalent circuit, apply Kirchoff Voltage Law

VP
 VS  Req I S  jX eq I S
k
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Phasor diagram of transformer referred to
the secondary

A F
O
D

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Voltage regulation at lagging power
factor
 Vs is taken as the reference phasor
 Is lags behind V2 by angle Φ
 IsReq is in phase with IS and IsXeq leads Is by 900
 Es (= ) is the phasor sum of VS, IsReq and IsXeq

 From right angled triangle: OFC

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 Voltage regulation at lagging
power factor
It follows:

The term, is small compared with the term,

and can be neglected

The approximate value of Es therefore becomes:

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Voltage regulation at lagging
power factor
EsVs Vs  I s Re coss  X e sins Vs
Per _ unit _VR  
Vs Vs

I s Re coss  X e sins 

VR 
Vs

I s Re coss  X e sins 

Percentage _VR  x100%
Vs

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Voltage regulation for different power
factor loads
For lagging loads, VP / a > VS so the voltage regulation with lagging loads
is > 0.

When the power factor is unity, VS is lower than VP so VR > 0.

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 Voltage regulation for different power
factor loads
With a leading power factor, VS is higher than the referred VP so VR < 0

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 Transformer Tests
The transformer tests are performed to
determine the circuit constants, efficiency
and voltage regulation
We distinguish between two typical tests:
- Open Circuit Test (O.C test / No load test)
- Short Circuit Test (S.C test/Impedance test)
These tests are economical and convenient

These tests furnish the result without actually

loading the transformer 24
 Open-circuit test

 secondary winding(usually the high voltage side) is

open-circuited, and its primary winding is connected to
a full-rated line voltage at rated frequency.
 A voltmeter V, an ammeter A and a wattmeter W are
connected in the low voltage (LV) side
 Since the secondary is open circuited, a very small
current I0 (usually 2 to 5% of rated current) called no-
load current, flows in the primary.
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 Open-circuit test
 Power loss in the transformer is due to core loss
and negligible copper loss, I2R in the primary
winding
 There is no I2R loss in the secondary since it is
open and Is = 0.
 The readings of the instruments are as follows:
Ammeter reading = no-load current I0
Voltmeter reading = primary rated voltage Vs
Wattmeter reading = iron or core loss Pi
 From these measured values components of the
no-load equivalent circuit can be determined.

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 Open-circuit test

(a) Core loss (b) No-load power factor

(c) Active component of I0 (d) Reactive component of I0

(e) Core loss resistance R0 (f) Magnetising reactance X0

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 Short-circuit Test

 secondary terminals (usually the low voltage side)

are short circuited by a thick conductor or through
an ammeter.
 An ammeter, a voltmeter and a wattmeter are
connected on the high-voltage side.
 The input voltage is gradually adjusted until full
load flows. 28
 Short-circuit Test
The readings of the instruments in the short-
circuit test are as follows:
Ammeter reading = full-load primary current,Isc
Voltmeter reading = short circuit voltage,Vsc
Wattmeter reading = full-load copper losses, Pcfl
The output voltage Vs is zero because of the
short circuit.
Consequently, the whole primary voltage is
used to supply the voltage drop in the total
impedance Z1e referred to the primary:
Vsc = IscZe
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 Short-circuit Test
If cosΦsc = power factor at short circuit then:
Pc = V1scI1sccosΦsc
Psc  I sc2 Re
Psc
Equivalent resistance referred to the primary: Re  2
I sc
Vsc
:Equivalent impedance referred to the primary Ze 
I sc

Equivalent reactance referred to the primary: X e  Z e2  Re2

Re
cossc 
Ze
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 Transformer Ratings
Transformers are rated to supply a given
output in
Volt Amps or VA
at a specified frequency and terminal
voltage.

They are NOT RATED in Watts. WHY????

because the load power factor is unknown

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 Transformer losses
 The transformer losses are classified into electrical
losses (copper losses) and Magnetic losses (Iron losses).
 Copper losses occur in both the primary and secondary
windings.
Pcu  I1 R1  I 2 R2
2 2

 Magnetic losses are divided into eddy current losses

and hysteresis losses.

Pcore  Peddy  Physterises

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 Copper losses (Pcu)
Varies with square of load current:

Produces HEAT.
Caused by resistance of windings.
Determine by Short Circuit Test
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 Core loss or iron loss
 Independent of the load
 Produces HEAT.
 Determined by Open Circuit Test.
 Eddy current loss is minimised by using
laminations.
 Hysteresis loss minimised by using silicon
steel.

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Behavior of magnetic losses and efficiency with loading
1.4
Cu Losses η%
1.2
Losses (W)

1.0
Fe Losses 97.00
0.8

0.6
η%
0.4

0.2

0.0 96.00
0 10 20 30 40 50 60 70 80 90 100 110
% Load

Condition for Maximum Efficiency: Fe = Cu =Max η

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 Transformer efficiency

Power Power
In Out

Overcome Overcome
Some Power Copper
is used to: Iron
Losses Losses
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 Efficiency
Efficiency is normally expressed as a percentage:

Output Power
η%   100
Input Power

VS I S cos 
 x100%
PCu  Pcore  VS I S cos 

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 All Day Efficiency
 The primary of a distribution transformer is
connected to the line for 24 hours a day.
 Thus the core losses occur for the whole day
whereas copper losses occur only when the
transformer is on load.
 Distribution transformers operate well below the
rated power output for most of the time.
 Performance of the distribution transformer is more
appropriately represented by all day efficiency.
 The all-day efficiency of a transformer is defined as
the ratio of total energy output for a certain period to
the total energy input for the same period.
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 All day efficiency
The energy efficiency can be calculated for a specified
period.
When the energy efficiency is calculated for a 24 hours it
is called the all-day efficiency.
out put in watts
Ordinary commercial efficiency 
input in watts

output in kWh
All  day  efficiency :all day  ( for 24 hours)
Input in kWh

All day efficiency is always less than the commercial efficiency

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AUTOTRANSFORMERS

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